Spartan is a SNARK for R1CS that can be instantiated with any multilinear polynomial commitment scheme. We instantiate Spartan over a binary field, using Ligerito as the commitment scheme along with the ring-switching technique of Diamond and Posen; we refer to the instantiation as BinarySpartan. It is transparent, so it requires no trusted setup, and it provides polylogarithmic-sized proofs. Its security rests on a hash function, so it is plausibly post-quantum. We apply well-known optimizations to Spartan and sum-check: the SIMD R1CS of Phalanx; the next multilinear extension of SuperSpartan; sum-check optimizations from Gruen, from Dao and Thaler, and from Bagad, Dao, Domb, and Thaler; and Binius64\u2019s byte lookup tables, which speed up the prover\u2019s early rounds of Spartan\u2019s outer sum-check. All but the last optimization were developed in the context of prime fields and in fact over large prime fields in the elliptic curve group setting. Furthermore, they are widely used in modern Spartan implementations. Thus, BinarySpartan is a natural instantiation of Spartan over binary fields.<\/p>\n\n\n\n
We implement and evaluate BinarySpartan end to end. On a MacBook Pro M4 Max (using only its 12 performance cores, and without GPU\/Metal acceleration), BinarySpartan proves BLAKE3 at 547,000 hashes\/second and SHA-256 at 255,000 hashes\/second, including witness generation. These clear the 200,000 hashes\/second rate proposed as sufficient for a post-quantum Ethereum transition, as well as the roughly 30,000\u2013180,000 hashes\/second a possible post-quantum Bitcoin transition would require. We also evaluate BinarySpartan on the Ethereum Foundation\u2019s client-side proving benchmark, where it proves a single SHA-256 of a 2 KiB message in 6.2 ms, making it the fastest scheme in the benchmark suite.<\/p>\n","protected":false},"excerpt":{"rendered":"
Spartan is a SNARK for R1CS that can be instantiated with any multilinear polynomial commitment scheme. We instantiate Spartan over a binary field, using Ligerito as the commitment scheme along with the ring-switching technique of Diamond and Posen; we refer to the instantiation as BinarySpartan. 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